In the case of Claude or others, it is not just an advertisement, it's the weird shape the industry is spinning LLM-assisted-coding as a "co-author" relationship where it should be thought of more like a user-using-a-tool relationship. When you make a design with Photoshop or InDesign, it's not "co-designed by Photoshop", it's just a tool and you used the filters it provides.
It is slightly weird that people accepted this new trend just like that, probably because they think this is being transparent and wanting to give attribution, but it'd be more useful like what the Linux kernel "AI Coding Assistants" page describes, something like `AGENT_NAME:MODEL_VERSION [TOOL1] [TOOL2]`, at least we get to know which model was used and/if any additional tooling on top. And `Assisted-by:` is more appropriate for that purpose than `Co-authored-by`.